The possible magnetic states of orthorhombic weak ferromagnets and rare-earth orthoferrites (REOF), the change of the magnetic state with the change of the temperature, and the mechanism of the formation of a new magnetic phase nucleus from a 180' domain wall for the first-order phase transition are considered. The AE-effect for both the first order phase transition and the transition by the reversible rotation of the antiferromagnetic vector and the magnetic susceptibility tensor, connected with the displacement of 90' domain walls, are calculated.